Logging in to Today is simple. Students just need to log in using their Google account and they will be ready to go. Make sure that the Google account that they are using to sign up for Today is the same one that they use to access Google Classroom.
You can send your students an invite by logging into your Today account and selecting the students that you would like to invite.
Also, Today is available on the G Suite Marketplace. This means that your G Suite domain administrator can install Today for every user in the domain, in which case everyone will automatically have access to Today.